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Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm

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Abstract

Heston model is the most famous stochastic volatility model in finance. This paper considers the parameter estimation problem of Heston model with both known and unknown volatilities. First, parameters in equity process and volatility process of Heston model are estimated separately since there is no explicit solution for the likelihood function with all parameters. Second, the normal maximum likelihood estimation (NMLE) algorithm is proposed based on the Itô transformation of Heston model. The algorithm can reduce the estimate error compared with existing pseudo maximum likelihood estimation. Third, the NMLE algorithm and consistent extended Kalman filter (CEKF) algorithm are combined in the case of unknown volatilities. As an advantage, CEKF algorithm can apply an upper bound of the error covariance matrix to ensure the volatilities estimation errors to be well evaluated. Numerical simulations illustrate that the proposed NMLE algorithm works more efficiently than the existing pseudo MLE algorithm with known and unknown volatilities. Therefore, the upper bound of the error covariance is illustrated. Additionally, the proposed estimation method is applied to American stock market index S&P 500, and the result shows the utility and effectiveness of the NMLE-CEKF algorithm.

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Authors and Affiliations

  1. Key Laboratory of System and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ximei Wang, Xingkang He & Yanlong Zhao

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Ximei Wang, Xingkang He & Yanlong Zhao

  3. Risk Management Department, Industrial and Commercial Bank of China, Beijing, 100033, China

    Ying Bao

Authors
  1. Ximei Wang
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  2. Xingkang He
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  3. Ying Bao
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  4. Yanlong Zhao
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Correspondence to Yanlong Zhao.

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Wang, X., He, X., Bao, Y. et al. Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm. Sci. China Inf. Sci. 61, 042202 (2018). https://doi.org/10.1007/s11432-017-9215-8

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